Statnote 15: the non-parametric correlation coefficients

If in a correlation test, one or both variables are small whole numbers, scores based on a limited scale, or percentages, a non-parametric correlation coefficient should be considered as an alternative to Pearson’s ‘r’. Kendall’s t and Spearman’s rs are similar tests but the former should be considered if the analysis is to be extended to include partial correlations. If the data contain many tied values, then gamma should be considered as a suitable test.

The effect of corruption on FDI:a parametric and non-parametric analysis

This paper analyses the effect of corruption on Multinational Enterprises' (MNEs) incentives to undertake FDI in a particular country. We contribute to the existing literature by modelling the relationship between corruption and FDI using both parametric and non-parametric methods. We report that the impact of corruption on FDI stock is different for the different quantiles of the FDI stock distribution. This is a characteristic that could not be captured in previous studies which used only parametric methods. After controlling for the location selection process of MNEs and other host country characteristics, the result from both parametric and non-parametric analyses offer some support for the ‘helping-hand’ role of corruption.

COOPER-framework:a unified process for non-parametric projects

Practitioners assess performance of entities in increasingly large and complicated datasets. If non-parametric models, such as Data Envelopment Analysis, were ever considered as simple push-button technologies, this is impossible when many variables are available or when data have to be compiled from several sources. This paper introduces by the 'COOPER-framework' a comprehensive model for carrying out non-parametric projects. The framework consists of six interrelated phases: Concepts and objectives, On structuring data, Operational models, Performance comparison model, Evaluation, and Result and deployment. Each of the phases describes some necessary steps a researcher should examine for a well defined and repeatable analysis. The COOPER-framework provides for the novice analyst guidance, structure and advice for a sound non-parametric analysis. The more experienced analyst benefits from a check list such that important issues are not forgotten. In addition, by the use of a standardized framework non-parametric assessments will be more reliable, more repeatable, more manageable, faster and less costly. © 2010 Elsevier B.V. All rights reserved.

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Clustering in non-parametric multivariate analyses.

Non-parametric multivariate analyses of complex ecological datasets are widely used. Following appropriate pre-treatment of the data inter-sample resemblances are calculated using appropriate measures. Ordination and clustering derived from these resemblances are used to visualise relationships among samples (or variables). Hierarchical agglomerative clustering with group-average (UPGMA) linkage is often the clustering method chosen. Using an example dataset of zooplankton densities from the Bristol Channel and Severn Estuary, UK, a range of existing and new clustering methods are applied and the results compared. Although the examples focus on analysis of samples, the methods may also be applied to species analysis. Dendrograms derived by hierarchical clustering are compared using cophenetic correlations, which are also used to determine optimum  in flexible beta clustering. A plot of cophenetic correlation against original dissimilarities reveals that a tree may be a poor representation of the full multivariate information. UNCTREE is an unconstrained binary divisive clustering algorithm in which values of the ANOSIM R statistic are used to determine (binary) splits in the data, to form a dendrogram. A form of flat clustering, k-R clustering, uses a combination of ANOSIM R and Similarity Profiles (SIMPROF) analyses to determine the optimum value of k, the number of groups into which samples should be clustered, and the sample membership of the groups. Robust outcomes from the application of such a range of differing techniques to the same resemblance matrix, as here, result in greater confidence in the validity of a clustering approach.

Non-invasive methodology for the identification of plastic pieces in museum environment – a novel approach

The preservation of modern and contemporary art and costume collections in museums requires a complete understanding of their constituent materials which are often synthetic or semi-synthetic polymers. An extraordinary amount of quality information can be gained from instrumental techniques, but some of them have the disadvantage of being destructive. This paper presents a new totally integrated non-invasive methodology, for the identification of polymers and their additives, on plastic artefacts in museums. NMR (nuclear magnetic resonance) and in-situ FTIR-ATR (attenuated total reflection infrared spectroscopy) combination allowed the full characterization of the structure of thesematerials and correct identification of each one. The NMR technique applied to leached surface exudates identified unequivocally a great number of additives, exceeding the Py–GC–MS analysis of micro-fragments in number and efficiency. Additionally, in-situ FTIR-ATR provided exactly the same information of the destructive μ-FTIR about the polymer structure and confirmed the presence of some additives. Eight costume pieces (cosmetic boxes and purses), dating to the beginning of the 20th century and belonging to the Portuguese National Museum of Costume and Fashion, were correctly identified with this new integrated methodology, as beingmade of plastics derived fromcellulose acetate or cellulose nitrate polymers, contradicting the initial information that these pieces were made of Bakelite. The identification of a surprisingly large number of different additives forms an added value of this methodology and opens a perspective of a quick and better characterization of plastic artefacts in museum environments.

Eficiencia técnica de las universidades argentinas de gestión estatal

Resumen: En el presente trabajo se examina la eficiencia técnica de las universidades argentinas de gestión estatal utilizando una metodología no paramétrica. A través del Análisis Envolvente de Datos se caracteriza a cada universidad mediante una única puntuación de eficiencia técnica relativa, lo que permite estimar las mejoras necesarias por comparación con un grupo de referencia. Se considera el modelo básico con orientación al producto, cuyos resultados muestran que las universidades tienen en promedio entre un 23,2% y un 23,9% de ineficiencia. Estos resultados son de utilidad para el diseño de políticas universitarias.

Impact of policy changes on the efficiency and returns-to-scale of Japanese financial institutions: an evaluation

This paper examines the impact of FSA's (Financial Services Agency) recent policy changes on the efficiency and returns-to-scale (RTS) of Japanese financial institutions including banks, securities companies and bank holding companies. Three kinds of efficiency are investigated namely, technical efficiency (TE), pure technical efficiency (PTE) and scale efficiency (SE) using the non-parametric methodology named data envelopment analysis (DEA). The DEA analysis shows a substantial improvement in the overall efficiency of Japanese banks, albeit a significant difference of efficiency scores between the major/city banks and the regional banks. Results are robust to alternative specifications of efficiency and scale changes.

Correlação entre medidas paramétricas e não-paramétricas de estabilidade em soja

Foram avaliadas a adaptabilidade e a estabilidade de genótipos de soja (Glycine max L.) segundo a metodologia clássica de Eberhart e Russell e a estabilidade dos mesmos genótipos pela metodologia não-paramétrica de Huhn. Os experimentos foram conduzidos no delineamento em blocos casualizados, com três repetições e com 30 tratamentos (genótipos de soja), durante três anos consecutivos. As parcelas experimentais foram constituídas por quatro linhas de cultivo, espaçadas de 0,50 m e com densidade de 25 plantas por metro linear. Como área útil, foram tomadas as linhas centrais, eliminando-se 0,5 m de cada extremidade. A comparação entre as metodologias foi efetuada considerando-se o caráter produção de grãos. Verificou-se correlação de posição significativa dos postos dos genótipos, entre o desvio da regressão e as duas medidas não-paramétricas de estabilidade, porém o mesmo não foi observado entre o coeficiente de regressão e as medidas não-paramétricas (Si(1) e Si(2)). As medidas Si(1) e Si(2) mostraram-se quase que perfeitamente correlacionadas.

Restricting the flexibility in DEA models

DEA models have been applied as the benchmarking tool in operations management to empirically account operational and productive efficiency. The wide flexibility in assigning the weights in DEA approach can result on indicators of efficiency who do not take account the relative importance of some inputs. In order to overcome this limitation, in this research we apply the DEA model under restricted weight specification. This model is applied to Spanish hotel companies in order to measure operational efficiency. The restricted weight specification enables us to decrease the influence of assigning unrealistic weights in some units and improve the efficiency estimation and to increase the discriminating potential of the conventional DEA model.

The reasons behind the progression in PISA scores: An education production function approach using semi-parametric techniques

Research Masters

New insights into methodology and interpretation of osteoarthritis. The study of Frassetto identified skeletal collection.

Osteoarthritis (OA) or degenerative joint disease (DJD) is a pathology which affects the synovial joints and characterised by a focal loss of articular cartilage and subsequent bony reaction of the subcondral and marginal bone. Its etiology is best explained by a multifactorial model including: age, sex, genetic and systemic factors, other predisposing diseases and functional stress. In this study the results of the investigation of a modern identified skeletal collection will be presented. In particular, we will focus on the relationship between the presence of OA at various joints. The joint modifications have been analysed using a new methodology that allows the scoring of different degrees of expression of the features considered. Materials and Methods The sample examined comes from the Sassari identified skeletal collection (part of “Frassetto collections”). The individuals were born between 1828 and 1916 and died between 1918 and 1932. Information about sex and age is known for all the individuals. The occupation is known for 173 males and 125 females. Data concerning the occupation of the individuals indicate a preindustrial and rural society. OA has been diagnosed when eburnation (EB) or loss of morphology (LM) were present, or when at least two of the following: marginal lipping (ML), esostosis (EX) or erosion (ER), were present. For each articular surface affected a “mean score” was calculated, reflecting the “severity” of the alterations. A further “score” was calculated for each joint. In the analysis sexes and age classes were always kept separate. For the statistical analyses non parametric test were used. Results The results show there is an increase of OA with age in all the joints analyzed and in particular around 50 years and 60 years. The shoulder, the hip and the knee are the joints mainly affected with ageing while the ankle is the less affected; the correlation values confirm this result. The lesion which show the major correlation with age is the ML. In our sample males are more frequently and more severely affected by OA than females, particularly at the superior limbs, while hip and knee are similarly affected in the two sexes. Lateralization shows some positive results in particular in the right shoulder of males and in various articular surfaces especially of the superior limb of both males and females; articular surfaces and joints are quite always lateralized to the right. Occupational analyses did not show remarkable results probably because of the homogeneity of the sample; males although performing different activities are quite all employed in stressful works. No highest prevalence of knee and hip OA was found in farm-workers respect to the other males. Discussion and Conclusion In this work we propose a methodology to score the different features, necessary to diagnose OA, that allows the investigation of the severity of joint degeneration. This method is easier than the one proposed by Buikstra and Ubelaker (1994), but in the same time allows a quite detailed recording of the features. Epidemiological results can be interpreted quite simply and they are in accordance with other studies; more difficult is the interpretation of the occupational results because many questions concerning the activities performed by the individuals of the collection during their lifespan cannot be solved. Because of this, caution is suggested in the interpretation of bioarcheological specimens. With this work we hope to contribute to the discussion on the puzzling problem of the etiology of OA. The possibility of studying identified skeletons will add important data to the description of osseous features of OA, enriching the medical documentation, based on different criteria. Even if we are aware that the clinical diagnosis is different from the palaeopathological one we think our work will be useful in clarifying some epidemiological as well as pathological aspects of OA.

Trust and strong ties in the selection and evaluation of business advisors by small firms

Principal Topic A small firm is unlikely to possess internally the full range of knowledge and skills that it requires or could benefit from for the development of its business. The ability to acquire suitable external expertise - defined as knowledge or competence that is rare in the firm and acquired from the outside - when needed thus becomes a competitive factor in itself. Access to external expertise enables the firm to focus on its core competencies and removes the necessity to internalize every skill and competence. However, research on how small firms access external expertise is still scarce. The present study contributes to this under-developed discussion by analysing the role of trust and strong ties in the small firm's selection and evaluation of sources of external expertise (henceforth referred to as the 'business advisor' or 'advisor'). Granovetter (1973, 1361) defines the strength of a network tie as 'a (probably linear) combination of the amount of time, the emotional intensity, the intimacy (mutual confiding) and the reciprocal services which characterize the tie'. Strong ties in the context of the present investigation refer to sources of external expertise who are well known to the owner-manager, and who may be either informal (e.g., family, friends) or professional advisors (e.g., consultants, enterprise support officers, accountants or solicitors). Previous research has suggested that strong and weak ties have different fortes and the choice of business advisors could thus be critical to business performance) While previous research results suggest that small businesses favour previously well known business advisors, prior studies have also pointed out that an excessive reliance on a network of well known actors might hamper business development, as the range of expertise available through strong ties is limited. But are owner-managers of small businesses aware of this limitation and does it matter to them? Or does working with a well-known advisor compensate for it? Hence, our research model first examines the impact of the strength of tie on the business advisor's perceived performance. Next, we ask what encourages a small business owner-manager to seek advice from a strong tie. A recent exploratory study by Welter and Kautonen (2005) drew attention to the central role of trust in this context. However, while their study found support for the general proposition that trust plays an important role in the choice of advisors, how trust and its different dimensions actually affect this choice remained ambiguous. The present paper develops this discussion by considering the impact of the different dimensions of perceived trustworthiness, defined as benevolence, integrity and ability, on the strength of tie. Further, we suggest that the dimensions of perceived trustworthiness relevant in the choice of a strong tie vary between professional and informal advisors. Methodology/Key Propositions Our propositions are examined empirically based on survey data comprising 153 Finnish small businesses. The data are analysed utilizing the partial least squares (PLS) approach to structural equation modelling with SmartPLS 2.0. Being non-parametric, the PLS algorithm is particularly well-suited to analysing small datasets with non-normally distributed variables. Results and Implications The path model shows that the stronger the tie, the more positively the advisor's performance is perceived. Hypothesis 1, that strong ties will be associated with higher perceptions of performance is clearly supported. Benevolence is clearly the most significant predictor of the choice of a strong tie for external expertise. While ability also reaches a moderate level of statistical significance, integrity does not have a statistically significant impact on the choice of a strong tie. Hence, we found support for two out of three independent variables included in Hypothesis 2. Path coefficients differed between the professional and informal advisor subsamples. The results of the exploratory group comparison show that Hypothesis 3a regarding ability being associated with strong ties more pronouncedly when choosing a professional advisor was not supported. Hypothesis 3b arguing that benevolence is more strongly associated with strong ties in the context of choosing an informal advisor received some support because the path coefficient in the informal advisor subsample was much larger than in the professional advisor subsample. Hypothesis 3c postulating that integrity would be more strongly associated with strong ties in the choice of a professional advisor was supported. Integrity is the most important dimension of trustworthiness in this context. However, integrity is of no concern, or even negative, when using strong ties to choose an informal advisor. The findings of this study have practical relevance to the enterprise support community. First of all, given that the strength of tie has a significant positive impact on the advisor's perceived performance, this implies that small business owners appreciate working with advisors in long-term relationships. Therefore, advisors are well advised to invest into relationship building and maintenance in their work with small firms. Secondly, the results show that, especially in the context of professional advisors, the advisor's perceived integrity and benevolence weigh more than ability. This again emphasizes the need to invest time and effort into building a personal relationship with the owner-manager, rather than merely maintaining a professional image and credentials. Finally, this study demonstrates that the dimensions of perceived trustworthiness are orthogonal with different effects on the strength of tie and ultimately perceived performance. This means that entrepreneurs and advisors should consider the specific dimensions of ability, benevolence and integrity, rather than rely on general perceptions of trustworthiness in their advice relationships.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.